Question

what is the horizontal displacement of the basic graph to produce a graph of y=pi-3cos(x-2) ?

a) pi units right
b) 3 units left
c) 2 units right
d) 2 units left

Answer 1

y = a sin b(x±h) ± k

a : amplitude => take absolute value

b : angular frequency

h : horizontal shift ( phase shift). (+ left, - right)

k : mid. line or vertical shift ( + up, - down)

period: the length of one cycle

period = 2π/b ( for sines, cosines. if tangent : p = π/b)